Oscillation for Higher Order Dynamic Equations on Time Scales
We investigate the oscillation of the following higher order dynamic equation: {an(t)[(an-1(t)(⋯(a1(t)xΔ(t))Δ⋯)Δ)Δ]α}Δ+p(t)xβ(t)=0, on some time scale T, where n≥2, ak(t) (1≤k≤n) and p(t) are positive rd-continuous functions on T and α,β are the quotient of odd positive integers. We give sufficien...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/268721 |
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| _version_ | 1832552030173921280 |
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| author | Taixiang Sun Qiuli He Hongjian Xi Weiyong Yu |
| author_facet | Taixiang Sun Qiuli He Hongjian Xi Weiyong Yu |
| author_sort | Taixiang Sun |
| collection | DOAJ |
| description | We investigate the oscillation of the following higher order dynamic equation: {an(t)[(an-1(t)(⋯(a1(t)xΔ(t))Δ⋯)Δ)Δ]α}Δ+p(t)xβ(t)=0, on some time scale T, where n≥2, ak(t) (1≤k≤n) and p(t) are positive rd-continuous functions on T and α,β are the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero. |
| format | Article |
| id | doaj-art-92b771a16e784080ad7678e5f9afd1c9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-92b771a16e784080ad7678e5f9afd1c92025-02-03T05:59:44ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/268721268721Oscillation for Higher Order Dynamic Equations on Time ScalesTaixiang Sun0Qiuli He1Hongjian Xi2Weiyong Yu3College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaCollege of Electrical Engineering, Guangxi University, Nanning, Guangxi 530004, ChinaDepartment of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaWe investigate the oscillation of the following higher order dynamic equation: {an(t)[(an-1(t)(⋯(a1(t)xΔ(t))Δ⋯)Δ)Δ]α}Δ+p(t)xβ(t)=0, on some time scale T, where n≥2, ak(t) (1≤k≤n) and p(t) are positive rd-continuous functions on T and α,β are the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.http://dx.doi.org/10.1155/2013/268721 |
| spellingShingle | Taixiang Sun Qiuli He Hongjian Xi Weiyong Yu Oscillation for Higher Order Dynamic Equations on Time Scales Abstract and Applied Analysis |
| title | Oscillation for Higher Order Dynamic Equations on Time Scales |
| title_full | Oscillation for Higher Order Dynamic Equations on Time Scales |
| title_fullStr | Oscillation for Higher Order Dynamic Equations on Time Scales |
| title_full_unstemmed | Oscillation for Higher Order Dynamic Equations on Time Scales |
| title_short | Oscillation for Higher Order Dynamic Equations on Time Scales |
| title_sort | oscillation for higher order dynamic equations on time scales |
| url | http://dx.doi.org/10.1155/2013/268721 |
| work_keys_str_mv | AT taixiangsun oscillationforhigherorderdynamicequationsontimescales AT qiulihe oscillationforhigherorderdynamicequationsontimescales AT hongjianxi oscillationforhigherorderdynamicequationsontimescales AT weiyongyu oscillationforhigherorderdynamicequationsontimescales |